Question: $A$ $B$ $C$ If: $ BC = 7x + 4$, $ AC = 86$, and $ AB = 8x + 7$, Find $BC$.
Answer: From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {8x + 7} + {7x + 4} = {86}$ Combine like terms: $ 15x + 11 = {86}$ Subtract $11$ from both sides: $ 15x = 75$ Divide both sides by $15$ to find $x$ $ x = 5$ Substitute $5$ for $x$ in the expression that was given for $BC$ $ BC = 7({5}) + 4$ Simplify: $ {BC = 35 + 4}$ Simplify to find ${BC}$ : $ {BC = 39}$